Evaluation of coupling coordination development between digital economy and green finance: Evidence from 30 provinces in China

The convergence of China’s digital economy and green finance holds great significance for fostering a sustainable and high-quality developmental path. However, existing studies have not explored the coupling coordination development between these two crucial subsystems. To bridge this gap, this paper employs a modified coupling coordination degree (CCD) model to assess and affirm the coupling coordination degree between the digital economy and green finance across 30 provinces in China from 2015–2021. Based on degree results, provinces are classified into three clusters by using K-means and hierarchical clustering algorithm. Our findings unveil that the current level of coupling coordination development in China is at a primary coordination stage. Although regional disparities significantly exist, the overall level of coordination remains steadily increasing, with the eastern region outperforming the western region. Additionally, we determine that the COVID-19 pandemic’s disruption on the coupling coordination development of these systems has been limited. This research sheds light on the evolution of coupling systems and offers practical recommendations for strengthening the coordinated development of the digital economy and green finance.


Introduction
In recent times, the development of the digital economy has significantly contributed to promoting economic growth and optimizing and upgrading the economic structure [1].For instance, China's digital economy expanded to 39.2 trillion yuan in 2020, contributing significantly to its GDP [2].Additionally, China's 14th Five-Year Plan emphasized the significance of green development and acknowledged green finance as a crucial component of the economy [3,4].Green finance is an effective mechanism for mitigating carbon emissions and promoting the progression of a low-carbon economy [5][6][7].However, the development of green finance encounters challenges such as inadequate technology and insufficient data [8].The integration of the digital economy with green finance mitigates these challenges and enhances contributions toward sustainable development [9].Therefore, studying the coupling coordination development between the digital economy and green finance is a crucial research topic that contributes to China's transition towards high-quality sustainable development.
With the growing integration of the digital economy and green finance, they are progressively coupling to foster high-quality economic growth.The digital economy's digital platforms and technological tools find widespread application in the realm of green finance, primarily focusing on green technology innovation, decision-making in green finance, and management of green supply chain.For instance, digital technology enables financial institutions to provide innovative services rooted in big data and artificial intelligence, including risk assessment, green bond issuance, and carbon emission trading, which serves as the groundwork for the innovation of green finance [10].In addition, Digital platforms, such as MSPs, can facilitate research, development, and promotion of green technologies through a range of services, including funding, sales channel management, and business intelligence solutions [11].
The relationship between the digital economy and green finance has emerged as a prominent area of research, with scholars exploring two key aspects.Some scholars considered that the digital economy played a significant role in enhancing the efficiency of green finance.Tian et al. (2022) [12] and Han et al. (2023) [13] believed that the digital economy had the potential to enhance the efficiency of output, resource allocation, and resource utilization in green finance.Zhang et al. (2022) [14] suggested that the development level of the digital economy and the total factor productivity index of the green economy had a positive correlation, showing the potential of the digital economy for promoting and enhancing the efficiency of green finance.Guo et al. (2022) [15] believed that the digital economy was also an great platform for applying green finance, which could more accurately allocate funds to the fields of environmental protection and sustainable development, thereby optimizing resource allocation and improving the efficiency of green finance.Some scholars had researched how the digital economy stimulated innovation in green finance.They primarily argued that digital technology such as digital finance could enhance the efficiency and quality of green innovation.Lin et al. (2022) [16] considered that digital technology could mitigate financing constraints for enterprises, upgrade industrial structure, consequently enhancing the capacity for regional green technology innovation.The empirical research conducted by Sun and Lin (2022) [17] revealed that the utilization of digital technology has a substantial impact on the advancement of green innovation in enterprises.Digital technology could reduce internal and external expenses, leading to increased profitability, and thus facilitating the acquisition of financial resources for green innovation.Zhao and Qian (2023) [18] discovered the heterogeneity in the impact of digital technology on green innovation in terms of human capital, R&D intensity, and environmental regulation.The study brought to light that regions with high-level talents, high R&D intensity, and stringent environmental regulations experience a significantly higher improvement effect on green innovation performance.In addition to promoting green innovation through digital technology, some scholars asserted digital transformation could facilitate green innovation.Xue et al. (2022) [19] contended that a company's digital transformation could significantly drive innovation in green technology by improving the digitization level of its data and accessibility to information, as well as enhancing the dissemination of external information.According to Zhang et al. (2023) [20], empirical research revealed that companies could increase their green dynamic capability, which enabled them to respond more quickly to market demands and environmental changes via digital transformation, leading to advancements in green technological innovation.
The phrase coupling usually refers to the interconnectedness between two entities that exhibit mutual influence and interaction [21].The theory of coupling portrays system relationships distinctively and quantifies the degree of relationship, known as the coupling degree (CD).The coupling degree represents the consistency and agreement between systems, demonstrating how the system changes from chaos to order following system contact [22].However, the coupling degree only characterizes the degree of interaction between systems, ignoring the capacity level of each system [23,24].The coupling coordination degree (CCD), nevertheless, considers not only the degree of interaction between systems, but also their coordination and balance.For instance, Gan et al. (2020) [25] examined the degree of coupling coordination between urbanization and industrial development in China through CCD model.Li et al. (2022) [26] utilized the CCD model to assess the ecological-economic coupling coordination index in northern China while delving into the driving factors that impact its coordination.However, the coupling coordination values calculated using the traditional CCD model may have an uneven distribution, which is unable to resolve the issue of the gap between system reliability and effectiveness.Thus, this paper utilizes a modified CCD model to measure the coupling and coordination between digital economy and green finance in order to more reasonably assess the level of coupling coordination and system development for each system [27].
With the gradual infusion of digital elements into the green industry, digital technology and digital platforms of the digital economy have emerged as the core elements of the development of green finance.By enhancing the digital foundation of green finance development, digital technology makes up for its technological limitations.However, current researches have mainly examined the significance and influence of the relationship between the digital economy and green finance.There are few studies discerning their logical nexus and regional disparities from a coupling perspective.Therefore, elucidating the coupling and coordination relationship between the digital economy and green finance has become a significant topic.Specifically, this study aims to answer the following questions: 1. Based on theoretical analysis, how does the coupled system comprising the digital economy subsystem and the green finance subsystem operate?
2. By establishing a modified CCD model, whether it can be validated that digital economy subsystem and green finance subsystem have a coupling and coordination relationship?
3. Has the evolution of the coupled system reached a definitive conclusion?If not, are there different stages of coupling coordination and, if so, what types of variation are present?
In order to answer these questions, this study establishes evaluation metrics and constructs a modified CCD model to evaluate the CD and CCD.On one hand, by utilizing coupling theory as the analytical framework, a novel coupled system is constructed, elucidating the main logical relationships and mechanism.On the other hand, based on the analysis results of CD and CCD, examinations are conducted regarding the trends of change and regional disparities.Furthermore, a clustering analysis of the 30 provinces is conducted based on the CCD over the past few years.Ultimately, recommendations are proposed concerning the coupling and coordination development of the digital economy and green finance.
The structure of this paper is as follows: Section 2 provides a review of the existing research on the relationship between the digital economy and green finance, examining it from two perspectives.Section 3 presents a theoretical analysis of the coupling mechanism, focusing on the digital economy subsystem and the green finance subsystem.Section 4 establishes a comprehensive evaluation index system to assess the CD and the CCD.It also introduces the main models utilized in this study.Section 5 discusses and analyzes the empirical results derived from the evaluation index system.Section 6 proposes countermeasures and suggestions for promoting the coupling coordination development between the digital economy and green finance.Section 7 summarizes the key findings and draws three main conclusions.Additionally, it discusses the innovation and limitations of this paper.

Literature review
The integration of the digital economy and green finance contributes to promoting sustainable and high-quality economic development.Digital technology innovation enables the interaction and connection between green finance and digital technology, leading to a transformation from a traditional risk management approach into a value enhancer that fosters sustainable development.Digital technology enhances data analysis and evaluation methods for green finance, thereby promoting the development of green industries.Consequently, the coordinated development of the digital economy and green finance has become a hot research topic within the academic community.
The existing literature has studied the relationship between digital economy and green finance from various perspectives, which can be organized into two major themes through sorting and summarizing, as follows.
Regarding the significance of digital economy to the development of green finance, some scholars suggested that the efficiency, transparency, and feasibility of green finance can be improved through the application of digital technology of digital economy, which can further promote sustainable development and the rational utilization of resources.The advancement of digital technology has substantially improved the efficiency and transparency of green finance.Wang et al. (2022) [28] claimed that the utilization of digital economic technology, for instance, employing big data and artificial intelligence to evaluate environmental risks and opportunities, could enhance the efficiency, feasibility, and transparency of green finance.Digital technology can help promote the financing of green finance.Li et al. (2021) [29] and Ozili (2022) [30] pointed out that the digital economy provided various new financing methods and platforms, such as green bonds, crowdfunding, and digital currencies that could facilitate the financing of green projects and enterprises.In addition, the digital economy significantly promotes the innovation of green financial products and services.Han and Liu (2022) [31] pointed out that the development of the digital economy offered opportunities for innovating green finance.For instance, the application of smart contracts and blockchain technology could improve the traceability and verifiability of green financial products.Likewise, by leveraging technologies such as artificial intelligence and blockchain, the processes involved in green finance could also be optimized, ensuring information transparency, risk control, and efficiently managing investment and financing, as well as improving fund utilization [32].What's more, Zhuang et al. (2022) [33] and Liu et al. (2023) [34] proposed that regulatory agencies and financial institutions played critical roles in the era of the digital economy, because they were responsible for establishing digital financial standards and guidelines, in addition to offering digital financial products and services to promote the growth of green finance.
Scholars have extensively examined the influence of digital finance on green finance.As a pivotal component of the digital economy, digital finance has redefined the conventional financial framework by means of tools such as online payment, mobile payment, electronic banking, and digital currencies [35].This transformation holds profound implications for green finance, particularly concerning resource utilization and innovation.Digital finance substantially enhances resource utilization efficiency while concurrently curbing environmental pollution.The application of digital technology and innovative approaches facilitated by digital finance, as underscored by Liu et al. (2022) [36], facilitates intelligent management of energy and water resources, leading to reduced consumption and the advancement of green energy solutions.Wu et al. (2023) [37] emphasize the imperative adoption of digital finance technologies by green financial institutions, broadening user scenarios and expanding the range of green financial services, thereby steering resources towards sustainable industries.Moreover, the symbiotic relationship between digital finance and innovations in green technology enhances the efficiency of carbon emission reduction efforts [38].However, the impact of digital finance on green efficiency is multifaceted.Excessive advancements can potentially introduce risks that impede energy efficiency [39].
In summary, scholars have predominantly examined the significance and relationship of the digital economy and green finance.However, research is limited on the coordinated relationship between them and regional development variations.In addition, limited research exists on the pathways of their coordinated development and the related quantitative assessments.What's more, there is no study that have conducted in-depth research on the logical relationship and regional variations surrounding the coupled coordination development of the digital economy and green finance.
Therefore, this study has established an evaluation index system and constructed relevant models to assess the coupling and coordination relationship between the digital economy and green finance, as well as to further examine the provincial development disparities in China.
To achieve this, we first constructed an analytical framework based on system theory and coupling theory to clarify the logical relationship and mechanism of the coupled system.Subsequently, by utilizing the analysis results of the coupling degree (CD) and coupling coordination degree (CCD), our study has examined trend changes and regional variability, providing valuable recommendations for the coupled development of the digital economy and green finance.

Theoretical analysis of coupled system
The relationship between the development of the digital economy and green finance is not entirely independent, parallel, contradictory, or incompatible.Instead, it represents a fusion and mutually reinforcing connection.This study builds upon system theory [40] and coupling theory [41] to examine the larger system as a coupled system consisting of the subsystems of the digital economy and green finance.It is a coupled entity formed through the interaction of elements and forces within the system.
To unveil the coupling relationship between the digital economy and green finance, it is essential to elucidate their interactions and the pathways that connect them.The digital economy represents a novel economic form, with data resources at its core, which are primarily disseminated and applied through modern information networks; Information and communication technologies (ICTs) play a crucial role in driving the development of the digital economy [42].Existing researches have outlined three key aspects of the digital economy: digital industrialization, industrial digitalization, and digitized infrastructure.Consequently, the coupling and coordination between the digital economy and green finance can be attained through three primary dimensions: industry coupling, technology coupling, and mindset coupling, as shown in Fig 1 .This synergistic coupling has the potential to advance high-quality and sustainable economic development.

Industry coupling
The similarities in the developmental processes of the digital economy and green finance signify the possibility for synergistic development between the digital industry and the green industry [15].Firstly, both the digital economy and green finance undergo development by transforming and integrating traditional industries.The digital economy utilizes digital information and communication technologies to enhance efficiency and optimize economic structures; Meanwhile, green finance centers on financial activities and investments that support environmentally sustainable projects and initiatives.Secondly, the development of both the digital economy and green finance relies on the construction of their respective infrastructures.The digital economy necessitates infrastructure construction such as fiber optic cables, mobile phone networks, and communication base stations.Similarly, the development of green finance also requires infrastructure, including renewable energy facilities, green power generation plants, and the establishment of green transportation systems.
The digital economy, through digital industrialization, brings new technologies, business models, and dynamics to traditional industries [43].On the other hand, green finance, through green industrialization, introduces new concepts, pathways, and models to traditional industries [44].These two aspects synergistically work together to promote the upgrading and transformation of traditional industry structures.The digital economy and green finance optimize the allocation of traditional production factors such as capital, labor, land, and knowledge technology, while promoting the integration between different industries through technological and innovative models [45].This enables traditional industries to not only have technological support, data support, and algorithmic empowerment but also possess characteristics of being greener, more rational, and higher-end.The development of the digital economy and green finance has given rise to a new type of IT industry based on digital technology that is pollution-free and environmentally friendly.It has also driven the development of emerging green industries such as new energy vehicles.The development demands of these new industries further stimulate digital and green innovation, creating a virtuous cycle and an economic multiplier effect [46].

Technology coupling
Through the process of industrial digitalization, digital technology has the potential to enhance the efficiency of traditional industries, reduce product costs, and address the problem of information asymmetry.Simultaneously, the adoption of green technology has played a vital role in industrial transformation by boosting energy efficiency, curbing pollution emissions, and facilitating resource allocation through sustainable practices [47,48].These advancements have brought about substantial transformations in industrial development and have had a positive impact on sustainable growth.The synergistic development of digital technology and green technology has the potential to enhance resource utilization efficiency, optimize production processes, and facilitate intelligent and sustainable solutions [49].For instance, the utilization of Internet of Things (IoT) sensors can enable monitoring and control of energy consumption, waste management systems, and emissions.This, in turn, allows for effective resource utilization and reduction of environmental impacts.In addition, the integration of digital technology and green technology has resulted in a notable decrease in environmental pollution during product manufacturing.Furthermore, digital services have replaced resource-intensive activities in various domains.For instance, the adoption of cloud services has the potential to substantially reduce energy consumption and carbon emissions.By hosting business applications on remote servers, energy consumption can be reduced by up to 80%, while the use of renewable energy sources can cut carbon emissions by as much as 96%.Emerging technologies like 3D printing, agricultural robots, and smart irrigation have significantly enhanced resource utilization efficiency and sustainability in production and operations [50].They have also contributed to the replacement and reduction of harmful gas emissions, along with improved waste recycling and utilization.What's more, big data and artificial intelligence technologies can be extensively utilized to acquire ecological and environmental information, addressing the issue of information asymmetry among polluters, victims, and regulators [51].Moreover, these technologies can accurately align consumers' demand for green products, optimize the allocation of product resources, facilitate the integration of market supply and demand, and unlock the potential purchasing power of consumers [52].

Mindset coupling
The coupling of the digital mindset and the green mindset is beneficial for achieving highquality and sustainable economic development.As these mindsets intertwine, they place higher demands on economic progress.The green mindset acknowledges the interdependence between humans and nature, perceiving the environment and humans as integral parts of a symbiotic system.Within this system, growth and development hold distinct meanings; Growth implies a quantitative increase, while development emphasizes the enhancement of quality [53].Secondly, green technology is playing a pivotal role in shifting the focus of the digital economy from a 'price-oriented' mindset to a more holistic 'value-oriented' approach, with sustainability at its core.As we navigate the path towards a sustainable digital economy, a triangular dilemma emerges, encompassing the crucial aspects of "security, speed, and energy consumption".However, attaining optimal levels of all three factors simultaneously proves to be an unattainable goal.In most cases, the resolution lies in finding a delicate equilibrium between security and speed, even if it results in higher energy consumption [54].Within the realm of the digital economy, green technology assumes a pivotal role as it seamlessly incorporates environmentally conscious practices.Unlike the conventional price-oriented perspective typically adopted by the economic system, green technology acknowledges the critical importance of the natural environment in which the system operates.By considering the ecosystem as a whole, this approach surpasses the limitations associated with a purely market-driven integration of technology, thus overcoming its inherent drawbacks.Thirdly, as the green paradigm permeates various aspects of corporate supply chains, a significant shift is underway, transitioning from the conventional "production rationality" to an emerging "ecological rationality" in the realm of production [55].The notion of green development has gained substantial momentum, leading to an increased environmental consciousness and literacy among individuals.Consequently, the concept of "greenness" is evolving into a broader and more encompassing "green perspective", reflecting a deeper understanding and commitment to environmentally sustainable practices.

Construction of the index system
To explore the coupling and coordination relationship between the digital economy subsystem and the green finance subsystem, it is essential to establish an evaluation index system.Taking into account the research conducted by Su et al. (2022) [56] and Wang et al. (2021) [57] and adhering to principles of scientific rigor, rationality, comprehensiveness, and operability, we have developed an evaluation index system for the selection of indicators.
Currently, there is no unified standard in the academic community to measure the level of digital economic development.However, several studies have proposed evaluation indicator systems.For example, Liu et al. (2020) [58] decomposed the digital economy index into three dimensions: informatization development indicators, internet development indicators, and digital transaction development indicators, using a total of 14 measurement indicators.Li et al. (2022) [59] guided by the new development concept of "innovation, coordination, greenness, openness, and sharing", selected 55 indicators to evaluate the level of digital economic development from these five aspects.Yang et al. (2022) [60] compiled a digital economy input-output table based on the "Classification of Digital Economy and its Core Industries (2021)" published by the National Bureau of Statistics, using it as an evaluation indicator system for the digital economy.Xu et al. (2023) [61] constructed a digital economic evaluation indicator system from five aspects: digital infrastructure, digital innovation capability, and digital coverage breadth.Yang et al. (2023) [62] constructed an evaluation indicator system for the digital economy based on eight aspects: digital economic development carriers, digital economic development environment, and digital economic development benefits.This paper utilizes established evaluation indicator systems and incorporates the CSMAR digital economic research module to formulate a comprehensive evaluation indicator framework for the digital economy.The framework is built upon three dimensions: digital industrialization [63], industrial digitalization [64], and technological innovation foundation, as shown in Table 1.The subsystem of digital economy development constructed in this paper includes seven sub-criterion layer and 32 indicators.
Currently, there is no unified standard for evaluating indicators in the field of green finance.Jiang et al. (2020) [65] constructed an evaluation system for green finance by selecting  [72], taking into account the current status of green finance and ecological civilization construction in Shandong Province, selected eight indicators from four dimensions: green investment, green credit, green insurance, and green securities to measure the level of green finance development.
Therefore, this study draws on the research of previous scholars and considers data availability.This paper selects five indicators from three dimensions: green securities, green investment market, and carbon market for constructing the evaluation indicators, as shown Table 2.

Research methods
Various methods exist for constructing indices, including AutoML [73], TOPSISS [74], and the relative importance index [75], etc..In this paper, the factor analysis model and entropy weight method are utilized to calculate the digital economy index and green finance index.Factor analysis is a classical statistical method extensively employed to extract latent factors that underlie the data.This method enables the identification of the most pertinent and representative factors from a vast array of indicators, thereby enhancing the effectiveness of capturing key characteristics of the digital economy [76].The entropy weight method is a multiindicator weight determination approach specifically designed to tackle the uncertainties and subjectivity associated with indicators [77].
Digital economy index and green finance index serve as the basis for assessing the coupling coordination degree between the digital economy and green finance, employing a modified CCD model.Furthermore, the K-means clustering analysis algorithm is applied to classify and analyze the development level of coupling coordination among 30 provinces in China, based on the results of the coupling coordination degree analysis.The analytical process is shown in Fig 2 .4.2.1 Factor analysis model.Considering the large number of evaluation indicators in the field of digital economy and taking into account the advantages of factor analysis models, this paper selects the factor analysis model to calculate the digital economic index (U 1 ).Factor analysis is a statistical technique employed to streamline and scrutinize datasets characterized by high dimensionality.By effectively transforming numerous observed variables, also known as indicators, into a reduced set of latent factors, this method facilitates a more concise representation of the data.Such dimensionality reduction serves to simplify the subsequent analysis and interpretation processes, while also mitigating the computational complexity associated with subsequent analytical procedures [78].The specific calculation steps are as follows:

Data standardization
In this paper, the Z-score method is used to standardize the raw data to transform them into dimensionless index measures.The formula is as follows: 2. Calculate the correlation coefficient matrix R for variables The formula is as follows: Where r ii = 1, r ij = r ij , and r ij represents the correlation coefficient between the i-th and j-th indicators in the formula.3. Calculate the elementary loading matrix.

Extract common factors
We need to calculate the contribution rate (w) of each common factor based on the elementary loading matrix and extract m principal factors.This paper employs probabilistic principal component analysis (PPCA) as a method to extract common factors.In comparison to traditional principal component analysis (PCA), PPCA presents several advantages, including enhanced flexibility, interpretability, and robustness [79,80].

Rotate the extracted factor loading matrix
To better comprehend the connotations conveyed by the common factors, the component matrix is orthogonally rotated using Kaiser's normalized maximum variance method [81], formula as followed: Based on the rotation, factor model is constructed.6. Calculate factor scores Factor scores are calculated by regression method, formula as shown: 4.2.2Entropy weight method (EWM).Due to the limited number of evaluation indicators for green finance, this paper utilizes the EWM to calculate the green finance index (U 2 ).EWM is an objective way to give weights based on the entropy value provided by the standardized values, specifically by measuring the degree of differentiation to assess the indicator's value [82].EWM is calculated as follows: 1. Standardize data with the following formula: For positive indicators: For negative indicators: In this paper, the standardized data is shifted to prevent the zero value from making the logarithm meaningless.Namely Z ij = S ij × 0.998 + 0.002.2. Measure the weight Y ij of indicator j in year i by the following formula: 3. The following equation is used to calculate the information entropy of the jth indicator: 4. Use this formula to get the entropy redundancy of the jth indicator: 5. The following formula is used to calculate the weight of the jth indicator: 6.The standardized data of each indicator is multiplied and summed with the weights:

Modified coupling coordination degree (CCD) model.
The interpretation of the coupling degree C relies on its interval distribution, and the values calculated by the traditional coupling model may exhibit uneven distribution, thereby diminishing its validity.To address this issue, this paper follows the methodology proposed by Wang [27] and establishes the modified CCD model as outlined below: C ¼ ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi where T represents the combined development of green finance and the digital economy, U 1 represents the digital economy index, and U 2 is green finance index.D is the CCD.Since the digital economy and green finance complement each other, it is considered α = 0.5, β = 0.5.
According to the study of Liu [83], Table 3 outlines the six levels that make up the CCD.

Clustering algorithm of machine learning.
Cluster analysis is a type of unsupervised learning in machine learning, where the objective is to provide an explanation for the underlying nature of the data and the patterns being seen by gaining knowledge from unlabeled training examples.Common clustering analysis algorithms commonly employed in various fields include the K-means algorithm, hierarchical clustering algorithm, and Modularity clustering algorithm, among others.These algorithms find extensive applications in diverse domains.For example, Feng et al. (2020) [84] introduced a non-parametric K-means algorithm specifically tailored for analyzing economic data.In another study, Govender et al. (2020) [85] utilized both the K-means algorithm and hierarchical clustering algorithm to classify and analyze air pollution data.Li et al. (2022) [86] employed the modularity clustering analysis technique to identify clusters of research articles pertaining to prefabricated building, construction management, economic development, and ESG attributes.
This paper aims to perform a clustering analysis on the level of coupling coordination development across 30 provinces in China, based on the outcomes of CCD.The clustering analysis in this study falls under the realm of traditional numerical data clustering problems.Therefore, two algorithms, namely the K-means algorithm and hierarchical clustering algorithm, are adopted.The K-means clustering algorithm is specifically designed to partition data into K distinct clusters, optimizing the similarity within each cluster while minimizing the similarity between different clusters [87].It is particularly suitable for distance-based data clustering problems.Moreover, the K-means algorithm offers flexibility in adjusting the number of clusters (K) to meet specific requirements.By increasing or decreasing the value of K, the granularity of clustering results can be controlled, thus catering to practical needs [88].On the other hand, the hierarchical clustering algorithm provides an effective visualization of data and is applicable to various data types.The results of hierarchical clustering can be visually represented through a dendrogram, facilitating a clear understanding of the similarity and hierarchical structure among data points.This visualization aids in the interpretation and explanation of clustering outcomes.

Empirical results and discussion
In order to ensure statistical consistency and data availability, this study focuses on 30 provinces in China (excluding Tibet, Hong Kong, Macau, and Taiwan) as the research subjects.The analysis primarily relies on various data sources, including the "China Statistical Yearbook", "China Third Industry Statistical Yearbook", "China Electronic Information Industry Yearbook", "China Industrial Statistical Yearbook", "China Science and Technology Statistical Yearbook", provincial statistical yearbooks and bulletins, EPS Global Statistical Database, CSMAR Database, among others.To address any missing data for specific years, trend extrapolation or interpolation methods are employed to supplement the gaps and maintain data continuity.

Evaluation of digital economy index
Based on the calculation process outlined in section 4.2.1 on factor analysis, Python is utilized in this study to calculate the digital economy index for each province spanning the years 2015 to 2021, as shown in Fig 3 .The results of its descriptive statistics are shown as Table 4. From the analysis of Table 4, several observations can be made regarding the digital economy index in different years.From 2015 to 2021, the digital economy index displayed a consistent upward trajectory, with the average increasing gradually from 1.02 to 1.04.Similarly, the median exhibited progress from 0.80 in 2015 to 0.89 in 2021, signifying an incremental rise in the majority of provinces.Concurrently, the standard deviation decreased progressively from 0.67 in 2015 to 0.55 in both 2020 and 2021, indicating a diminishing level of volatility within the digital economy index throughout this period.However, there is a notable difference between the minimum and maximum values of the digital economy index, indicating significant disparities in digital economic development among the provinces.This reflects regional variations and disparities in terms of economic foundations, technological innovation capabilities, and levels of informatization.In summary, the digital economy index demonstrated an overall upward trend within this timeframe, although notable disparities persisted among different provinces.Our findings are similar to the research conducted by Zhang et al. (2021) [42] and Jiang et al. (2022) [89], who also mentioned that the overall development of digital economy in China is steady.Moreover, their research findings indicate that the growth of China's digital economy makes a substantial contribution to high-quality economic development.
In Fig 3, the depth of color corresponds to a higher level of the digital economy index.In terms of regional distribution, provinces located in the eastern coastal areas, such as Beijing, Shanghai, Jiangsu, and Zhejiang, exhibit higher digital economy indexes.These provinces benefit from their advanced economies, robust technological innovation ecosystems, and extensive implementation of information technology.On the other hand, provinces in the western regions, such as Guizhou, Yunnan, and Qinghai, have lower digital economy indexes.This discrepancy can be attributed to their relatively weaker economic foundations, limited technological innovation capacities, and comparatively lower levels of informatization.In a similar study, Tang et al. ( 2021) [90] and Li et al. (2022) [91] explored the digital economy index in China and identified comparable regional disparities, with coastal provinces displaying higher digital economy indexes in contrast to inland provinces.The consistency between their findings and ours enhances the validity of our results and emphasizes the importance of regional disparities in China's digital economic development.
Additionally, our analysis of Fig 3 and Table 4 indicates that the influence of the COVID-19 on the overall growth of China's digital economy has been relatively minimal.The consistent stability of the digital economy index over different years suggests that the digital sector has demonstrated resilience and adaptability, even in the face of the challenges posed by COVID-19.This finding aligns with the research conducted by Xu et al. (2022) [92], who also proposed that the rapid advancement of China's digital economy had mitigated the severity of the impact of COVID-19 on the Chinese economy.

Evaluation of green finance index
According to section 4.2.2 on entropy weight method, the results of green finance index and its descriptive statistics are shown as in Fig 4 and Table 5.From 2015 to 2021, the mean of the green finance index demonstrated a notable degree of stability, hovering around 0.30, thus depicting a state of sustained equilibrium.Conversely, the median experienced a minor decrease from 0.27 in 2015 to 0.26 in 2021, implying a potential marginal reduction in the green finance index within specific provinces.Additionally, the standard deviation exhibited a gradual increase from 0.15 in 2017 to 0.16 in 2021, hinting at a slight rise in the volatility of the green finance index during this timeframe.In conclusion, the green finance index exhibited a state of relative stability throughout this period, although divergences among different provinces continued to persist.
Regions with high levels of green finance development are primarily situated in the northeastern coastal areas, such as Shanghai, Beijing, Guangdong, and Zhejiang provinces.These regions boast higher levels of economic development, abundant economic resources, and stronger technological capabilities, which provide them with a significant advantage in green industries and sustainable development.They actively promote the advancement of environmentally friendly industries, facilitate the transition towards a low-carbon economy, and proactively introduce and nurture green financial institutions and projects.To contextualize our findings, we conducted a comparative analysis with the research conducted by He et al. (2020) [93] and Lin et al. (2023) [94], who also examined the development of green finance in China.Their study highlighted the concentration of green finance development in the northeastern coastal areas, aligning with our own findings.This consistency in results strengthens the reliability and validity of our research, further underscoring the significance of these regions in leading green finance initiatives.

Evaluation of the CCD
According to the section 4.2.3 on modified CCD model, the calculation results of CCD and its descriptive statistics are shown in Tables 6 and 7. Table 7 presents a comprehensive compilation of descriptive statistical data concerning the coupling coordination degree among the 30 provinces spanning the years 2015 to 2021.It is evident that within this dataset, a discernible trend emerges.Specifically, there is a gradual increase in the mean from 0.403 to 0.421 over the specified time frame.This progression strongly implies a noteworthy enhancement in the overall coupling coordination degree among the distinct provinces.Concurrently, the medians exhibit marginal annual fluctuations within the range of 0.369 to 0.405, aligning with the trajectory observed in the mean.Furthermore, across the 2015-2021 period, the standard  deviation demonstrates a progressive rise, ascending from 0.101 to 0.130.This phenomenon indicates an expanding diversity in coupling coordination across provinces, thus implying a progressively broader divergence among provinces over these years.Within the same temporal interval, the minimum value fluctuates between 0.253 and 0.243, while the maximum value experiences variations between 0.659 and 0.752.These fluctuations underscore substantial disparities in coupling coordination degree across diverse provinces and years.In summary, a comprehensive assessment reveals a discernible ascending trend in coupling coordination among provinces from 2015 to 2021.However, this trend is concurrently accompanied by a growing year-to-year variance.This phenomenon might indicate that developmental discrepancies among provinces have progressively widened over this specific time span, thereby instigating changes in coupling coordination degree.
From the Table 6 and Fig 5, it is apparent that the level of coordinated development between the digital economy and green finance varies significantly among different provinces.In the eastern region, provinces like Beijing, Shanghai, Zhejiang, and Guangdong stand out as top performers, surpassing the regional average and displaying steady growth in their level of coordination between the digital economy and green finance.Other provinces in this region, including Tianjin, Jiangsu, and Shandong, also exhibit favorable performance, albeit with some fluctuations in certain years.The central region presents a more diverse performance, with Henan showcasing significant progress in recent years, leading to noticeable improvement in its coordination level.Provinces like Anhui and Hunan have also shown some improvement, although their overall level remains relatively low.In the northeastern region, the performance is generally average.Liaoning province consistently falls below the regional average, while Heilongjiang and Jilin display less satisfactory performance in terms of coordination between the digital economy and green finance.The western region demonstrates varying levels of performance.Provinces like Sichuan and Shaanxi exhibit higher levels of coordination, while Gansu, Qinghai, and Xinjiang demonstrate relatively average performance.
In addition, based on the results, it seems that the COVID-19 has had a modest influence on the coupling coordination development between China's digital economy and green finance.The analysis reveals a slight decline in CCD across each region, indicating that the COVID-19 has impacted the level of coordination between these two sectors.The reasons behind this decline in CCD are likely multifaceted.The pandemic has disrupted economic activities, presenting challenges for the digital economy and green finance sectors.Factors such as reduced investments, shifts in consumer behavior, and disruptions in supply chains may have affected the coordinated development between these sectors.
It is important to note that although the impact of COVID-19 on CCD is evident in the results, the decline appears to be relatively minor.This suggests that the digital economy and green finance sectors have demonstrated resilience and adaptability in the face of the challenges posed by COVID-19.Government efforts to mitigate the impact and facilitate recovery from the disruptions caused by COVID-19 may have contributed to the overall stability and gradual improvement observed in the coupling coordination development between the digital economy and green finance.
In summary, the descriptive statistical results indicate an increasing trend in the coordinated development between the digital economy and green finance in China's provinces.Provinces in the eastern region, such as Beijing, Shanghai, Zhejiang, and Guangdong, lead the way with notable progress.The central region shows a mixed performance, while the northeastern and western regions demonstrate varying levels of coordination.

Clustering analysis
According to the information provided in section 4.2.4,this paper employs a combination of the K-means algorithm and hierarchical clustering algorithm for the classification analysis of the coordinated development between China's digital economy and green finance.To evaluate the quality of the clustering results, the paper conducts silhouette analysis.Silhouette analysis calculates the silhouette coefficient for each sample, which quantifies the closeness of a sample to its own cluster compared to other clusters [95].A silhouette coefficient approaching 1 indicates that a sample has a small distance within its own cluster and a significant distance from other clusters, suggesting a favorable clustering result.Based on the computational results presented in the paper, when the number of clusters is set to 3, the analysis yields a good clustering outcome, as illustrated in Fig 6 .The average silhouette coefficient reaches its highest value of 0.537, indicating a relatively strong clustering result.This suggests that the samples within each cluster are closely related to one another, while there are notable differences between different clusters.Therefore, the clustering outcome at this particular setting is considered  innovation and development pilot zones have been established in cities like Guangzhou and Shenzhen.These zones actively focus on the artificial intelligence industry.Moreover, Guangdong province encourages and guides social capital to establish green development funds and carbon funds to support green and low-carbon projects.Therefore, the level of coupling and coordination between the digital economy and green finance in these regions is steadily improving.
The provinces included in the second cluster, namely Tianjin, Hebei, Liaoning, Anhui, Fujian, Shandong, Henan, Hubei, Hunan, Sichuan, and Shaanxi, exhibit a CCD between their digital economy and green finance at approximately 0.4, indicating that they are in the primary stage of coordination.Despite the relatively low coupling degree, these provinces have demonstrated a positive trend of stable growth over the past seven years.To facilitate the development of the digital economy, these provinces prioritize the creation of favorable conditions.They actively promote digital innovation capabilities and accelerate the digital transformation of their respective industries.By embracing digital technologies and fostering innovation, these regions aim to enhance productivity, competitiveness, and overall economic growth.Moreover, these provinces make investments in green finance and closely monitor its development and challenges.Recognizing the importance of sustainable finance, they establish multi-level green finance policies and service platforms.These initiatives facilitate the coordinated development of green finance across regions, based on unified industry standards.By aligning their efforts, these provinces foster a synergistic approach to green finance, contributing to sustainable economic growth and environmental protection.Overall, while these provinces may have a relatively lower level of coordination between the digital economy and green finance, they have shown positive progress and stability in their development.Their focus on creating favorable conditions, promoting digital innovation, and investing in green finance demonstrates their commitment to achieving a more coordinated and sustainable approach to economic development.
The third cluster includes Shanxi, Inner Mongolia, Jilin, Heilongjiang, Jiangxi, Guangxi, Hainan, Chongqing, Guizhou, Yunnan, Gansu, Qinghai, and Xinjiang provinces.These provinces exhibit a low degree of CCD between the digital economy and green finance, nearly in the lowest level of coordination.Most of these regions have relatively lower levels of economic development and lack a foundation for nurturing the digital economy.They face challenges such as insufficient innovation capacity in key areas, relatively slow digitization of traditional industries, and the need to overcome the digital divide.Moreover, the governance system for the digital economy requires improvement.Additionally, the development level of green finance in these regions is relatively low, with inadequate product innovation capacity and limited market depth and breadth.The intermediary services for green finance development in these regions are also relatively weak.

Formulate differentiated regional development policies to narrow the gap in regional development
To rectify the disparity in the coordinated development of the digital economy and green finance across different regions in China, the policymaker should implement macro-level measures aimed at regulating and optimizing fiscal intervention.These measures seek to distribute policy resources more equitably and efficiently.
One specific measure involves strategically allocating policy resources to the central and western regions, which are comparatively less developed.The policymaker should increase investments in green technology innovation and digital infrastructure construction within these regions.By directing resources and support towards these areas, the objective is to stimulate their rapid development in the digital economy and green finance sectors.This approach aims to promote sustainable development and bridge the regional development gap within the country.
Through fostering the expansion of the digital economy and green finance in the central and western regions, the policymaker intends to ensure that all areas can benefit from the opportunities presented by these sectors.This approach fosters economic inclusivity by enabling regions with traditionally fewer advantages to participate and contribute to the overall development of the country.Additionally, it seeks to establish a more balanced and harmonized economic landscape, where the benefits and opportunities of the digital economy and green finance are distributed more evenly nationwide.
In summary, the government's macro-level measures prioritize leveraging fiscal intervention to address regional disparities in the coordinated development of the digital economy and green finance in China.By allocating policy resources towards the less developed central and western regions, increasing investments in green technology innovation and digital infrastructure, and promoting sustainable development, the policymaker aims to bridge the regional development gap, foster economic inclusivity, and ensure that all regions can benefit from the opportunities presented by the digital economy and green finance.

Promote the deep coordination of green development and digitalization
In the realm of production and consumption, businesses are increasingly recognizing the significance of utilizing digital technology to expand their range of green consumer products.This enables them to offer a broader selection of high-quality digital intelligent products that not only cater to but also guide the preferences of environmentally conscious consumers.Governments play a crucial role in facilitating this shift towards green consumption.
Governments should actively promote industrial digitization by leading efforts to enhance the integration of front-end and back-end industries.This involves collaborating with upstream and downstream enterprises to reduce resource consumption during production and minimize pollution emissions throughout the consumption process.Through active engagement with stakeholders and the implementation of effective policies, governments can drive economic development towards technological advancement and encourage the adoption of environmentally friendly products.
However, it is important to acknowledge that while the digital economy brings notable penetrability and significant economies of scale, it also carries environmental implications of its own.The substantial energy consumption and carbon dioxide emissions associated with the digital economy must not be overlooked.Therefore, it becomes imperative for us to establish a green consensus and mitigate redundant consumption resulting from the digital transformation process in order to ensure sustainable development.
By embracing sustainable practices and striving for resource efficiency, both businesses and governments can effectively address the environmental impact of the digital economy.This necessitates a comprehensive approach that encompasses the development and promotion of green consumer products, as well as the implementation of policies and measures to minimize the ecological footprint of digital technologies.
In conclusion, the integration of digital technology with green production and consumption is vital for driving economic growth and achieving sustainability goals.Through digital innovation, businesses can diversify their product offerings to meet the needs of environmentally conscious consumers.Simultaneously, governments must actively promote industrial digitization and collaborate with industry stakeholders to reduce resource consumption and pollution emissions.By establishing a green consensus and adopting sustainable practices, we can ensure that the process of digital transformation aligns with the principles of green development and contributes to a more environmentally friendly future.

Conclusions
In this study, both factor analysis modeling and the entropy weight method were employed to calculate and analyze the digital economy index and the green finance index of various provinces.Based on the index outcomes, a modified coupling coordination degree model was formulated to assess and validate the disparities in coupling relationships and coordination levels between the two subsystems.Furthermore, to illuminate spatial and temporal variations in coupling coordination development across different regions, this study employed two clustering algorithms: K-means and hierarchical clustering.According to the findings presented in this research, 30 provinces were categorized into three clusters based on their coupling coordination degree.On a broader perspective, China's digital economy and green finance are presently undergoing coupling coordination development at a relatively modest level, positioned at the primary coordination stage.The coupling coordination development of the two subsystems, in general, demonstrated steady growth; however, there were pronounced regional disparities among provinces.Specifically, the level of coupling coordination development in the eastern regions was comparatively higher than that in the western regions.Likewise, coastal areas exhibited higher level of coupling coordination development compared to inland regions.Remarkably, despite the impact of COVID-19, the coupling coordination development of the two subsystems displayed resilience, showcasing an overall upward trend.
This study makes significant contributions in both theoretical and practical aspects.Theoretical expansion is achieved by extending the research scope of coupling theory to encompass the digital economy and green finance.In terms of practical implications, the study enriches the application of the digital economy and green finance through the use of the modified coupling coordination model to analyze the degree, evolutionary stages, and trends of their coupling coordination.Additionally, based on the research findings, we can put forth several policy recommendations to facilitate the coupling coordination development between digital economy and green finance in China, such as formulate region-specific development policies, support green technology innovation and digital infrastructure, promote industrial digitization and collaboration and establish a consensus on green practices.
While this study demonstrates innovation, there are limitations attributed to factors such as time constraints and data availability.The evaluation index system may also have limitations, despite employing a rigorous selection process and a substantial number of evaluation indicators.Further consideration is necessary to address the issue of indicator deviation, which may require calibration and improvement in different environments or provinces.Moreover, the study only analyzes 30 provinces in China due to data availability, posing limitations in terms of representativeness.Future research could expand the sample range to include a broader range of regions, such as urban and rural areas, in order to obtain more comprehensive and accurate research results.

Table 1 . Evaluation index system of the digital economy.
[71] et al. (2022)economic, financial, and social.Yu et al. (2021)[66] developed an evaluation system to comprehensively measure the level of green finance development, focusing on four green financial instruments: green credit, green bonds, green investment, and carbon finance.Qiao et al. (2021)[67]andZhou et al. (2022)[68]divided green finance into five subcategories: green credit, green securities, green insurance, green investment, and carbon finance, and constructed indicator systems accordingly.Wang (2022)[69]andZheng (2022)[70]constructed evaluation indicator systems for green finance based on three macro aspects: environment, finance, and society.Zeng et al. (2022)[71]utilized metrics such as carbon intensity as indicators for evaluating the performance of green supply chains, effectively measuring the manifestation of environmentally sustainable development.Zhang et al. (2023) https://doi.org/10.1371/journal.pone.0291936.t001relevant indicators from